I think what you’re thinking of @chris.williamson1996 is my Floppy plugin which writes values to various forms of browser storage. You could use this as an alternative to writing a value on Current User, but I’m not sure why you’d do that. (Floppy does not write cookies, which are not the correct way to store persistent local values these days.)
But the OP’s question isn’t about “cookies” per se, they are just throwing terms around. If some new user (browser) arrives at a Bubble site, that visitor is assigned a Current User which does persist for some time. (And yeah, that’s probably managed via a cookie, but you don’t access it that way.) You can just write some flag on the Current User when they dismiss the Annoying Popup (and you don’t show the popup if Current User has the Dismissed Annoying Popup flag set to yes).
Now, writing a value to localStorage would be persistent until that value is specifically cleared in some way from that particular browser, so that would potentially be more persistent than relying on Current User (which will, in fact, change over time), but again “why?”. I wouldn’t focus on someone’s “first time” visit as important in any meaningful way. We instead think about the experience for the logged in vs non-logged in user, right?